Your iPhone SE should work just fine on the Vodafone NZ network - you should check a couple of things to make sure.
Look on the back cover to identify the model number. The model sold and supported in NZ is A1723.
Some phones are sold Network-locked. Check with your current network to make sure. If it is locked, arrange an unlock with them. iPhone models sold by Vodafone NZ are not network locked - I'd exepct that the same is true for yours.
Model A1662 will work on NZ Networks, but will not work with 4G Band 28 at 700MHz (the APT version).